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Real Numbers

Jharkhand Board · Class 10 · Mathematics

Step-by-step guide to study Real Numbers in Jharkhand Board Class 10 Mathematics. Topics to cover, practice strategy, and time allocation.

61 questions22 flashcards4 concepts

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A Venn diagram illustrating the classification of real numbers into rational and irrational numbers, with further subdivisions for rational numbers (integers, whole numbers, natural numbers).
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Study Plan

1
Day 1–2

Learn the Theory

Read the textbook chapter carefully. Note down definitions, formulas, and key concepts.

2
Day 3

Practice Problems

Solve textbook exercises and additional practice questions. There are 61 questions available for this chapter.

3
Day 4

Revise & Test

Revise key formulas and concepts without looking at notes. Take a practice quiz to test your understanding. Mark weak areas for re-revision.

4
Day 7

Spaced Revision

Revisit Real Numbers after a week. Use flashcards for quick recall. Solve previous year questions from this chapter.

What to Focus On

  • Every composite number has a unique prime factorisation (order doesn't matter).
  • The prime factorisation of 1 is empty — 1 is neither prime nor composite.
  • HCF uses the LOWEST powers of COMMON prime factors.

  • Proof by contradiction: Assume rational, derive contradiction, conclude irrational.
  • KEY THEOREM: If prime p divides a², then p divides a.
  • Always state 'a and b are coprime (HCF = 1)' at the start of the proof.

  • p/q terminates if and only if q (in lowest form) = 2ⁿ × 5ᵐ.
  • ALWAYS simplify the fraction to lowest form before checking.
  • If denominator has any prime factor other than 2 and 5, it is non-terminating repeating.

Common Mistakes to Avoid

1 is a prime number

If p divides a², then p divides a is always true for ANY integer p, not just primes

√(a×b) = √a × √b works for ALL real numbers, including negative numbers

Memory Tips

Fundamental Theorem of Arithmetic — Every composite number has a UNIQUE prime factorisation

Prime factorisation is the building block of all composite numbers

Factor Tree Method for Prime Factorisation

If p (prime) divides a², then p divides a (Theorem 1.2)

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Frequently Asked Questions

What are the important topics in Real Numbers for Jharkhand Board Class 10 Mathematics?
Key topics in Real Numbers include How to Correctly Identify Rational vs Irrational Numbers, Real Numbers Chapter — Complete Concept Map, Real Numbers — Complete Chapter Overview. These are the concepts Jharkhand Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Real Numbers — Jharkhand Board Class 10 Mathematics?
Understand the core concepts first, then work through the 61 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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